In the bowl of a small food processor, add the rosemary, thyme, garlic cloves, salt, pepper, and oil. Pulse just until the mixture comes together and the garlic is minced. Do not overprocess. You do not want a paste.
Set the Instant Pot to sauté mode. When it's hot, add a little oil, then sear the chuck roast on all sides, about 3 minutes per side, to develop flavor. Remove and set aside.
Pour the beef broth and red wine into the bowl of the Instant Pot. Place the mushrooms in the liquid and lay the seared roast on top of the mushrooms.
Spread the seasoning mixture over the top of the roast.
Close the lid and seal the vent. Cook on high pressure for 1 hour. Let the pressure naturally release for 15 minutes, then quick release any remaining steam. Press cancel when done.
Remove the roast from the pot and set it on a large cutting board or plate. Let the meat rest for 5-10 minutes before shredding.
Use a slotted spoon to remove the mushrooms from the pot and reserve them on a platter. Use two forks to shred the roast.
Strain the remaining juices through a fine sieve. Return the broth to the pot. Use the sauté function to bring the broth to a boil. Whisk in the xanthan gum until the liquid thickens into a gravy. Press cancel and transfer the gravy to a bowl or gravy boat.
Plate the shredded roast with the mushrooms and gravy. Garnish with fresh rosemary, if desired. Serve immediately.